you are building a rectanle deck. the area of the deck should be 250 ft^2. you want the length of the deck to be 5 ft longer than twice the width.

Question

what should the dimensions be?

Answer 1

Let the width be w. 

Then the length will be 5 + 2w or 2w + 5

Area of a rectangle = length x width

250 = (2w + 5)(w)

250 = 2w² + 5w

subtract 250 from both sides.

2w² + 5w - 250 = 0

Factor the trinomial.

(2w + 25) (w-10) = 0

Set each factor equal to 0

2w + 5 = 0 and w-10=0

2w = -5               w = 10

w = -2.5

The answer w = -2.5 is not a realistic answer because the width of a deck cannot be negative. 

So the only valid answer is w = 10.  The width is 10 feet and the length will be 2w + 5 = 2(10) + 5 = 25 feet.  Therefore the dimensions are 25 feet x 10 feet.